For the shrimp, remove the vein by using a small sharp knife to cut a shallow slit at the top back through the shell. Be careful when you cut as the shell is slippery. Transfer to a large bowl. Cover with plastic wrap and keep in the fridge.
Preheat the oven to 450˚F (230˚C). Coat the roasting pan with non-stick cooking spray.
In the pan, toss the potatoes with 1½ tablespoons of olive oil, and season with salt and pepper. Roast for 15 minutes, then flip with a spatula to ensure even browning.
In a small bowl, combine the remaining 1½ tablespoons of olive oil and the garlic, oregano, and Parmesan cheese, and season with salt and pepper. Add mixture to the shrimp. Toss well and make sure to massage the mixture into the open slit of the shrimp. Add the shrimp to the roasting pan. Roast for 5 minutes. Flip and roast for another 5 minutes, or until the shrimp is pink, firm and cooked through.
Leave it to cool slightly, then garnish with parsley and lemon wedges, if using, and serve.